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112-809: The main advantage of an electromagnet over a permanent magnet is that the magnetic field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a continuous supply of current to maintain the magnetic field. Electromagnets are widely used as components of other electrical devices, such as motors , generators , electromechanical solenoids , relays , loudspeakers , hard disks , MRI machines , scientific instruments, and magnetic separation equipment. Electromagnets are also employed in industry for picking up and moving heavy iron objects such as scrap iron and steel. Danish scientist Hans Christian Ørsted discovered in 1820 that electric currents create magnetic fields. In

224-471: A pacemaker has been embedded in a patient's chest (usually for the purpose of monitoring and regulating the heart for steady electrically induced beats ), care should be taken to keep it away from magnetic fields. It is for this reason that a patient with the device installed cannot be tested with the use of a magnetic resonance imaging device. Children sometimes swallow small magnets from toys, and this can be hazardous if two or more magnets are swallowed, as

336-401: A torque tending to orient the magnetic moment parallel to the field. The amount of this torque is proportional both to the magnetic moment and the external field. A magnet may also be subject to a force driving it in one direction or another, according to the positions and orientations of the magnet and source. If the field is uniform in space, the magnet is subject to no net force, although it

448-415: A combination of aluminium , nickel and cobalt with iron and small amounts of other elements added to enhance the properties of the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist corrosion and have physical properties more forgiving than ferrite, but not quite as desirable as

560-776: A common ground state in the manner of a Bose–Einstein condensate . The United States Department of Energy has identified a need to find substitutes for rare-earth metals in permanent-magnet technology, and has begun funding such research. The Advanced Research Projects Agency-Energy (ARPA-E) has sponsored a Rare Earth Alternatives in Critical Technologies (REACT) program to develop alternative materials. In 2011, ARPA-E awarded 31.6 million dollars to fund Rare-Earth Substitute projects. Iron nitrides are promising materials for rare-earth free magnets. The current cheapest permanent magnets, allowing for field strengths, are flexible and ceramic magnets, but these are also among

672-419: A curl states that the divergence of the curl of a vector field must always be zero. Hence and so the original Ampère's circuital law implies that i.e. that the current density is solenoidal . But in general, reality follows the continuity equation for electric charge : which is nonzero for a time-varying charge density. An example occurs in a capacitor circuit where time-varying charge densities exist on

784-418: A dielectric the above contribution to displacement current is present too, but a major contribution to the displacement current is related to the polarization of the individual molecules of the dielectric material. Even though charges cannot flow freely in a dielectric, the charges in molecules can move a little under the influence of an electric field. The positive and negative charges in molecules separate under

896-416: A different issue, however; correlations between electromagnetic radiation and cancer rates have been postulated due to demographic correlations (see Electromagnetic radiation and health ). If a ferromagnetic foreign body is present in human tissue, an external magnetic field interacting with it can pose a serious safety risk. A different type of indirect magnetic health risk exists involving pacemakers. If

1008-514: A given current, or the current associated with a given magnetic field. The original circuital law only applies to a magnetostatic situation, to continuous steady currents flowing in a closed circuit. For systems with electric fields that change over time, the original law (as given in this section) must be modified to include a term known as Maxwell's correction (see below). The original circuital law can be written in several different forms, which are all ultimately equivalent: The integral form of

1120-427: A high- coercivity ferromagnetic compound (usually ferric oxide ) mixed with a resinous polymer binder. This is extruded as a sheet and passed over a line of powerful cylindrical permanent magnets. These magnets are arranged in a stack with alternating magnetic poles facing up (N, S, N, S...) on a rotating shaft. This impresses the plastic sheet with the magnetic poles in an alternating line format. No electromagnetism

1232-432: A larger core must be used. However, computing the magnetic field and force exerted by ferromagnetic materials in general is difficult for two reasons. First, because the strength of the field varies from point to point in a complicated way, particularly outside the core and in air gaps, where fringing fields and leakage flux must be considered. Second, because the magnetic field B and force are nonlinear functions of

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1344-428: A limit on the maximum force per unit core area, or magnetic pressure , an iron-core electromagnet can exert; roughly: for saturation limit of the core, B sat . In more intuitive units it is useful to remember that at 1 T the magnetic pressure is approximately 4 atmospheres, or kg/cm. Given a core geometry, the B field needed for a given force can be calculated from (1); if it comes out to much more than 1.6 T,

1456-400: A loop or magnetic circuit , possibly broken by a few narrow air gaps. Iron presents much less "resistance" ( reluctance ) to the magnetic field than air, so a stronger field can be obtained if most of the magnetic field's path is within the core. Since the magnetic field lines are closed loops, the core is usually made in the form of a loop. Since most of the magnetic field is confined within

1568-571: A magnet can be magnetized with different directions and strengths (for example, because of domains, see below). A good bar magnet may have a magnetic moment of magnitude 0.1 A·m and a volume of 1 cm , or 1×10  m , and therefore an average magnetization magnitude is 100,000 A/m. Iron can have a magnetization of around a million amperes per meter. Such a large value explains why iron magnets are so effective at producing magnetic fields. Two different models exist for magnets: magnetic poles and atomic currents. Although for many purposes it

1680-410: A magnetic field around the wire, due to Ampere's law (see drawing of wire with magnetic field) . To concentrate the magnetic field in an electromagnet, the wire is wound into a coil with many turns of wire lying side by side. The magnetic field of all the turns of wire passes through the center of the coil, creating a strong magnetic field there. A coil forming the shape of a straight tube (a helix )

1792-410: A maximum pull of 8.75 pounds (corresponding to C = 0.0094 psi ). The maximum pull is increased when a magnetic stop is inserted into the solenoid. The stop becomes a magnet that will attract the plunger; it adds little to the solenoid pull when the plunger is far away but dramatically increases the pull when they are close. An approximation for the pull P is Here ℓ a is the distance between

1904-492: A metal. Trade names for alloys in this family include: Alni, Alcomax, Hycomax, Columax , and Ticonal . Injection-molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties. Flexible magnets are composed of

2016-402: A net contribution; shaving off the outer layer of a magnet will not destroy its magnetic field, but will leave a new surface of uncancelled currents from the circular currents throughout the material. The right-hand rule tells which direction positively-charged current flows. However, current due to negatively-charged electricity is far more prevalent in practice. The north pole of a magnet

2128-410: A north and south pole. However, a version of the magnetic-pole approach is used by professional magneticians to design permanent magnets. In this approach, the divergence of the magnetization ∇· M inside a magnet is treated as a distribution of magnetic monopoles . This is a mathematical convenience and does not imply that there are actually monopoles in the magnet. If the magnetic-pole distribution

2240-399: A partially occupied f electron shell (which can accommodate up to 14 electrons). The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore, these elements are used in compact high-strength magnets where their higher price is not a concern. The most common types of rare-earth magnets are samarium–cobalt and neodymium–iron–boron (NIB) magnets. In

2352-502: A particular direction, creating a microscopic current. When the currents from all these atoms are put together, they create the same effect as a macroscopic current, circulating perpetually around the magnetized object. This magnetization current J M is one contribution to "bound current". The other source of bound current is bound charge . When an electric field is applied, the positive and negative bound charges can separate over atomic distances in polarizable materials , and when

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2464-551: A permanent magnet has a large influence on its magnetic properties. When a magnet is magnetized , a demagnetizing field will be created inside it. As the name suggests, the demagnetizing field will work to demagnetize the magnet, decreasing its magnetic properties. The strength of the demagnetizing field H d {\displaystyle H_{d}} is proportional to the magnet's magnetization M {\displaystyle M} and shape, according to Here, N d {\displaystyle N_{d}}

2576-403: A piece of iron bridged across its poles, equation ( 2 ) becomes: Substituting into ( 1 ), the force is: It can be seen that to maximize the force, a core with a short flux path L and a wide cross-sectional area A is preferred (this also applies to magnets with an air gap). To achieve this, in applications like lifting magnets (see photo above) and loudspeakers a flat cylindrical design

2688-518: A simple magnetic dipole; for example, quadrupole and sextupole magnets are used to focus particle beams . Ampere%27s circuital law In classical electromagnetism , Ampère's circuital law (not to be confused with Ampère's force law ) relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper " On Physical Lines of Force ". In 1865 he generalized

2800-400: A strong magnetic field during manufacture to align their internal microcrystalline structure, making them very hard to demagnetize. To demagnetize a saturated magnet, a certain magnetic field must be applied, and this threshold depends on coercivity of the respective material. "Hard" materials have high coercivity, whereas "soft" materials have low coercivity. The overall strength of a magnet

2912-400: Is a lifting magnet. A tractive electromagnet applies a force and moves something. Electromagnets are very widely used in electric and electromechanical devices, including: A common tractive electromagnet is a uniformly-wound solenoid and plunger. The solenoid is a coil of wire, and the plunger is made of a material such as soft iron. Applying a current to the solenoid applies a force to

3024-566: Is an object made from a material that is magnetized and creates its own persistent magnetic field. An everyday example is a refrigerator magnet used to hold notes on a refrigerator door. Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic (or ferrimagnetic ). These include the elements iron , nickel and cobalt and their alloys, some alloys of rare-earth metals , and some naturally occurring minerals such as lodestone . Although ferromagnetic (and ferrimagnetic) materials are

3136-422: Is called a solenoid . The direction of the magnetic field through a coil of wire can be found from a form of the right-hand rule . If the fingers of the right hand are curled around the coil in the direction of current flow ( conventional current , flow of positive charge ) through the windings, the thumb points in the direction of the field inside the coil. The side of the magnet that the field lines emerge from

3248-416: Is called the demagnetizing factor, and has a different value depending on the magnet's shape. For example, if the magnet is a sphere , then N d = 1 3 {\displaystyle N_{d}={\frac {1}{3}}} . The value of the demagnetizing factor also depends on the direction of the magnetization in relation to the magnet's shape. Since a sphere is symmetrical from all angles,

3360-443: Is convenient to think of a magnet as having distinct north and south magnetic poles, the concept of poles should not be taken literally: it is merely a way of referring to the two different ends of a magnet. The magnet does not have distinct north or south particles on opposing sides. If a bar magnet is broken into two pieces, in an attempt to separate the north and south poles, the result will be two bar magnets, each of which has both

3472-579: Is defined as the pole that, when the magnet is freely suspended, points towards the Earth's North Magnetic Pole in the Arctic (the magnetic and geographic poles do not coincide, see magnetic declination ). Since opposite poles (north and south) attract, the North Magnetic Pole is actually the south pole of the Earth's magnetic field. As a practical matter, to tell which pole of a magnet

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3584-429: Is defined to be the north pole . For definitions of the variables below, see box at end of article. Much stronger magnetic fields can be produced if a " magnetic core " of a soft ferromagnetic (or ferrimagnetic ) material, such as iron , is placed inside the coil. A core can increase the magnetic field to thousands of times the strength of the field of the coil alone, due to the high magnetic permeability μ of

3696-432: Is due to the resistance of the windings, and is dissipated as heat. Some large electromagnets require water cooling systems in the windings to carry off the waste heat . Since the magnetic field is proportional to the product NI , the number of turns in the windings N and the current I can be chosen to minimize heat losses, as long as their product is constant. Since the power dissipation, P = I R , increases with

3808-405: Is highest for alnico magnets at over 540 °C (1,000 °F), around 300 °C (570 °F) for ferrite and SmCo, about 140 °C (280 °F) for NIB and lower for flexible ceramics, but the exact numbers depend on the grade of material. An electromagnet, in its simplest form, is a wire that has been coiled into one or more loops, known as a solenoid . When electric current flows through

3920-513: Is known, then the pole model gives the magnetic field H . Outside the magnet, the field B is proportional to H , while inside the magnetization must be added to H . An extension of this method that allows for internal magnetic charges is used in theories of ferromagnetism. Another model is the Ampère model, where all magnetization is due to the effect of microscopic, or atomic, circular bound currents , also called Ampèrian currents, throughout

4032-462: Is measured by its magnetic moment or, alternatively, the total magnetic flux it produces. The local strength of magnetism in a material is measured by its magnetization . An electromagnet is made from a coil of wire that acts as a magnet when an electric current passes through it but stops being a magnet when the current stops. Often, the coil is wrapped around a core of "soft" ferromagnetic material such as mild steel , which greatly enhances

4144-464: Is north and which is south, it is not necessary to use the Earth's magnetic field at all. For example, one method would be to compare it to an electromagnet , whose poles can be identified by the right-hand rule . The magnetic field lines of a magnet are considered by convention to emerge from the magnet's north pole and reenter at the south pole. The term magnet is typically reserved for objects that produce their own persistent magnetic field even in

4256-419: Is often used. The winding is wrapped around a short wide cylindrical core that forms one pole, and a thick metal housing that wraps around the outside of the windings forms the other part of the magnetic circuit, bringing the magnetic field to the front to form the other pole. The above methods are applicable to electromagnets with a magnetic circuit and do not apply when a large part of the magnetic field path

4368-417: Is outside the core. A non-circuit example would be a magnet with a straight cylindrical core like the one shown at the top of this article. Only focusing on the force between two electromagnets (or permanent magnets) with well-defined "poles" where the field lines emerge from the core, a special analogy called a magnetic-charge model which assumes the magnetic field is produced by fictitious 'magnetic charges' on

4480-408: Is possible. With the addition of the displacement current, Maxwell was able to hypothesize (correctly) that light was a form of electromagnetic wave . See electromagnetic wave equation for a discussion of this important discovery. Proof that the formulations of the circuital law in terms of free current are equivalent to the formulations involving total current In this proof, we will show that

4592-476: Is specified by two properties: In SI units, the strength of the magnetic B field is given in teslas . A magnet's magnetic moment (also called magnetic dipole moment and usually denoted μ ) is a vector that characterizes the magnet's overall magnetic properties. For a bar magnet, the direction of the magnetic moment points from the magnet's south pole to its north pole, and the magnitude relates to how strong and how far apart these poles are. In SI units,

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4704-400: Is subject to a torque. A wire in the shape of a circle with area A and carrying current I has a magnetic moment of magnitude equal to IA . The magnetization of a magnetized material is the local value of its magnetic moment per unit volume, usually denoted M , with units A / m . It is a vector field , rather than just a vector (like the magnetic moment), because different areas in

4816-432: Is the magnetic H field (also called "auxiliary magnetic field", "magnetic field intensity", or just "magnetic field"), D is the electric displacement field , and J f is the enclosed conduction current or free current density. In differential form, On the other hand, treating all charges on the same footing (disregarding whether they are bound or free charges), the generalized Ampère's equation, also called

4928-499: Is the number of turns in the solenoid, I is the current through the solenoid wire, and ℓ is the length of the solenoid. For units using inches, pounds force, and amperes with long, slender, solenoids, the value of C is around 0.009 to 0.010 psi (maximum pull pounds per square inch of plunger cross-sectional area). For example, a 12-inch long coil ( ℓ = 12 in ) with a long plunger of 1-square inch cross section ( A = 1 in ) and 11,200 ampere-turns ( N I = 11,200 Aturn ) had

5040-448: Is the polarization density . Substituting this form for D in the expression for displacement current, it has two components: The first term on the right hand side is present everywhere, even in a vacuum. It doesn't involve any actual movement of charge, but it nevertheless has an associated magnetic field, as if it were an actual current. Some authors apply the name displacement current to only this contribution. The second term on

5152-410: Is used to generate the magnets. The pole-to-pole distance is on the order of 5 mm, but varies with manufacturer. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used. For magnetic compounds (e.g. Nd 2 Fe 14 B ) that are vulnerable to a grain boundary corrosion problem it gives additional protection. Rare earth ( lanthanoid ) elements have

5264-402: Is why the very strongest electromagnets, such as superconducting and very high current electromagnets, cannot use cores. The main nonlinear feature of ferromagnetic materials is that the B field saturates at a certain value, which is around 1.6 to 2 teslas (T) for most high permeability core steels. The B field increases quickly with increasing current up to that value, but above that value

5376-456: The circulation of the magnetic field around some path (line integral) due to the current which passes through that enclosed path (surface integral). In terms of total current , (which is the sum of both free current and bound current) the line integral of the magnetic B -field (in teslas , T) around closed curve C is proportional to the total current I enc passing through a surface S (enclosed by C ). In terms of free current,

5488-515: The horseshoe magnet was invented by Daniel Bernoulli in 1743. A horseshoe magnet avoids demagnetization by returning the magnetic field lines to the opposite pole. In 1820, Hans Christian Ørsted discovered that a compass needle is deflected by a nearby electric current. In the same year André-Marie Ampère showed that iron can be magnetized by inserting it in an electrically fed solenoid. This led William Sturgeon to develop an iron-cored electromagnet in 1824. Joseph Henry further developed

5600-414: The 1850s Scottish mathematical physicist James Clerk Maxwell generalized these results and others into a single mathematical law. The original form of Maxwell's circuital law, which he derived as early as 1855 in his paper "On Faraday's Lines of Force" based on an analogy to hydrodynamics, relates magnetic fields to electric currents that produce them. It determines the magnetic field associated with

5712-429: The 1990s, it was discovered that certain molecules containing paramagnetic metal ions are capable of storing a magnetic moment at very low temperatures. These are very different from conventional magnets that store information at a magnetic domain level and theoretically could provide a far denser storage medium than conventional magnets. In this direction, research on monolayers of SMMs is currently under way. Very briefly,

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5824-595: The Earth's magnetic field would leave the iron permanently magnetized. This led to the development of the navigational compass , as described in Dream Pool Essays in 1088. By the 12th to 13th centuries AD, magnetic compasses were used in navigation in China, Europe, the Arabian Peninsula and elsewhere. A straight iron magnet tends to demagnetize itself by its own magnetic field. To overcome this,

5936-1190: The Maxwell–Ampère equation, is in integral form (see the " proof " section below): ∮ C B ⋅ d l = ∬ S ( μ 0 J + μ 0 ε 0 ∂ E ∂ t ) ⋅ d S {\displaystyle \oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {l}}=\iint _{S}\left(\mu _{0}\mathbf {J} +\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)\cdot \mathrm {d} \mathbf {S} } In differential form, ∇ × B = μ 0 J + μ 0 ε 0 ∂ E ∂ t {\displaystyle \mathbf {\nabla } \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}} In both forms J includes magnetization current density as well as conduction and polarization current densities. That is,

6048-689: The absence of an applied magnetic field. Only certain classes of materials can do this. Most materials, however, produce a magnetic field in response to an applied magnetic field – a phenomenon known as magnetism. There are several types of magnetism, and all materials exhibit at least one of them. The overall magnetic behavior of a material can vary widely, depending on the structure of the material, particularly on its electron configuration . Several forms of magnetic behavior have been observed in different materials, including: There are various other types of magnetism, such as spin glass , superparamagnetism , superdiamagnetism , and metamagnetism . The shape of

6160-440: The applied field, causing an increase in the state of polarization, expressed as the polarization density P . A changing state of polarization is equivalent to a current. Both contributions to the displacement current are combined by defining the displacement current as: where the electric displacement field is defined as: where ε 0 is the electric constant , ε r the relative static permittivity , and P

6272-660: The availability of magnetic materials to include various man-made products, all based, however, on naturally magnetic elements. Ceramic, or ferrite , magnets are made of a sintered composite of powdered iron oxide and barium / strontium carbonate ceramic . Given the low cost of the materials and manufacturing methods, inexpensive magnets (or non-magnetized ferromagnetic cores, for use in electronic components such as portable AM radio antennas ) of various shapes can be easily mass-produced. The resulting magnets are non-corroding but brittle and must be treated like other ceramics. Alnico magnets are made by casting or sintering

6384-467: The bound charges move, the polarization changes, creating another contribution to the "bound current", the polarization current J P . The total current density J due to free and bound charges is then: with J f   the "free" or "conduction" current density. All current is fundamentally the same, microscopically. Nevertheless, there are often practical reasons for wanting to treat bound current differently from free current. For example,

6496-403: The bound current usually originates over atomic dimensions, and one may wish to take advantage of a simpler theory intended for larger dimensions. The result is that the more microscopic Ampère's circuital law, expressed in terms of B and the microscopic current (which includes free, magnetization and polarization currents), is sometimes put into the equivalent form below in terms of H and

6608-459: The circuital equation is extended by including the polarization current, thereby remedying the limited applicability of the original circuital law. Treating free charges separately from bound charges, the equation including Maxwell's correction in terms of the H -field is (the H -field is used because it includes the magnetization currents, so J M does not appear explicitly, see H -field and also Note ): (integral form), where H

6720-446: The circuital law. James Clerk Maxwell conceived of displacement current as a polarization current in the dielectric vortex sea, which he used to model the magnetic field hydrodynamically and mechanically. He added this displacement current to Ampère's circuital law at equation 112 in his 1861 paper " On Physical Lines of Force ". In free space , the displacement current is related to the time rate of change of electric field. In

6832-404: The core material ( C ). Within the core the magnetic field ( B ) will be approximately uniform across any cross-section, so if in addition, the core has roughly constant area throughout its length, the field in the core will be constant. This leaves the air gaps ( G ), if any, between core sections. In the gaps, the magnetic field lines are no longer confined by the core. So they 'bulge' out beyond

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6944-423: The core's magnetization is constantly reversed, and the remanence contributes to the motor's losses. The magnetic field of electromagnets in the general case is given by Ampere's Law : which says that the integral of the magnetizing field H {\displaystyle \mathbf {H} } around any closed loop is equal to the sum of the current flowing through the loop. Another equation used, that gives

7056-515: The current density on the right side of the Ampère–Maxwell equation is: where current density J D is the displacement current , and J is the current density contribution actually due to movement of charges, both free and bound. Because ∇ ⋅  D = ρ , the charge continuity issue with Ampère's original formulation is no longer a problem. Because of the term in ε 0 ⁠ ∂ E / ∂ t ⁠ , wave propagation in free space now

7168-399: The current that passes through a wire or battery . In contrast, "bound current" arises in the context of bulk materials that can be magnetized and/or polarized . (All materials can to some extent.) When a material is magnetized (for example, by placing it in an external magnetic field), the electrons remain bound to their respective atoms, but behave as if they were orbiting the nucleus in

7280-403: The current, depending on the nonlinear relation between B and H for the particular core material used. For precise calculations, computer programs that can produce a model of the magnetic field using the finite element method are employed. In many practical applications of electromagnets, such as motors, generators, transformers, lifting magnets, and loudspeakers, the iron core is in the form of

7392-461: The demagnetizing factor only has one value. But a magnet that is shaped like a long cylinder will yield two different demagnetizing factors, depending on if it's magnetized parallel to or perpendicular to its length. Because human tissues have a very low level of susceptibility to static magnetic fields, there is little mainstream scientific evidence showing a health effect associated with exposure to static fields. Dynamic magnetic fields may be

7504-416: The electromagnet into a commercial product in 1830–1831, giving people access to strong magnetic fields for the first time. In 1831 he built an ore separator with an electromagnet capable of lifting 750 pounds (340 kg). The magnetic flux density (also called magnetic B field or just magnetic field, usually denoted by B ) is a vector field . The magnetic B field vector at a given point in space

7616-448: The end of the stop and the end of the plunger. The additional constant C 1 for units of inches, pounds, and amperes with slender solenoids is about 2660. The second term within the bracket represents the same force as the stop-less solenoid above; the first term represents the attraction between the stop and the plunger. Some improvements can be made on the basic design. The ends of the stop and plunger are often conical. For example,

7728-405: The entire core circuit, and thus will not contribute to the force exerted by the magnet. This also includes field lines that encircle the wire windings but do not enter the core. This is called leakage flux . The equations in this section are valid for electromagnets for which: The magnetic field created by an electromagnet is proportional to both N and I , hence this product, NI , is given

7840-478: The equation is equivalent to the equation Note that we are only dealing with the differential forms, not the integral forms, but that is sufficient since the differential and integral forms are equivalent in each case, by the Kelvin–Stokes theorem . We introduce the polarization density P , which has the following relation to E and D : Next, we introduce the magnetization density M , which has

7952-470: The equation to apply to time-varying currents by adding the displacement current term, resulting in the modern form of the law, sometimes called the Ampère–Maxwell law , which is one of Maxwell's equations that form the basis of classical electromagnetism . In 1820 Danish physicist Hans Christian Ørsted discovered that an electric current creates a magnetic field around it, when he noticed that

8064-438: The field disappears. However, some of the alignment persists, because the domains have difficulty turning their direction of magnetization, leaving the core magnetized as a weak permanent magnet. This phenomenon is called hysteresis and the remaining magnetic field is called remanent magnetism . The residual magnetization of the core can be removed by degaussing . In alternating current electromagnets, such as are used in motors,

8176-414: The field levels off and becomes almost constant, regardless of how much current is sent through the windings. The maximum strength of the magnetic field possible from an iron core electromagnet is limited to around 1.6 to 2 T. When the current in the coil is turned off, in the magnetically soft materials that are nearly always used as cores, most of the domains lose alignment and return to a random state and

8288-407: The field, and the magnetic field passes through the core in lower reluctance than when it would pass through air. The larger the current passed through the wire coil, the more the domains align, and the stronger the magnetic field is. Finally, all the domains are lined up, and further increases in current only cause slight increases in the magnetic field: this phenomenon is called saturation . This

8400-455: The first magnetic compasses . The earliest known surviving descriptions of magnets and their properties are from Anatolia, India, and China around 2,500 years ago. The properties of lodestones and their affinity for iron were written of by Pliny the Elder in his encyclopedia Naturalis Historia in the 1st century AD. In 11th century China, it was discovered that quenching red hot iron in

8512-403: The following ways: Magnetized ferromagnetic materials can be demagnetized (or degaussed) in the following ways: Many materials have unpaired electron spins, and the majority of these materials are paramagnetic . When the spins interact with each other in such a way that the spins align spontaneously, the materials are called ferromagnetic (what is often loosely termed as magnetic). Because of

8624-404: The free current only. For a detailed definition of free current and bound current, and the proof that the two formulations are equivalent, see the " proof " section below. There are two important issues regarding the circuital law that require closer scrutiny. First, there is an issue regarding the continuity equation for electrical charge. In vector calculus, the identity for the divergence of

8736-400: The iron has no large-scale magnetic field. When a current is passed through the wire wrapped around the iron, its magnetic field penetrates the iron, and causes the domains to turn, aligning parallel to the magnetic field, so their tiny magnetic fields add to the wire's field, creating a large magnetic field that extends into the space around the magnet. The effect of the core is to concentrate

8848-405: The line integral of the magnetic H -field (in amperes per metre , A·m ) around closed curve C equals the free current I f,enc through a surface S . There are a number of ambiguities in the above definitions that require clarification and a choice of convention. The electric current that arises in the simplest textbook situations would be classified as "free current"—for example,

8960-477: The magnetic field due to each small segment of current, is the Biot–Savart law . Likewise on the solenoid, the force exerted by an electromagnet on a conductor located at a section of core material is: The force equation can be derived from the energy stored in a magnetic field . Energy is force times distance. Rearranging terms yields the equation above. The 1.6 T limit on the field mentioned above sets

9072-613: The magnetic field produced by the coil. Ancient people learned about magnetism from lodestones (or magnetite ) which are naturally magnetized pieces of iron ore. The word magnet was adopted in Middle English from Latin magnetum "lodestone", ultimately from Greek μαγνῆτις [λίθος] ( magnētis [lithos] ) meaning "[stone] from Magnesia", a place in Anatolia where lodestones were found (today Manisa in modern-day Turkey ). Lodestones, suspended so they could turn, were

9184-403: The magnetic moment is specified in terms of A·m (amperes times meters squared). A magnet both produces its own magnetic field and responds to magnetic fields. The strength of the magnetic field it produces is at any given point proportional to the magnitude of its magnetic moment. In addition, when the magnet is put into an external magnetic field, produced by a different source, it is subject to

9296-623: The magnetomotive force is well above saturation, so the core material is in saturation, the magnetic field will be approximately the saturation value B sat for the material, and will not vary much with changes in NI . For a closed magnetic circuit (no air gap) most core materials saturate at a magnetomotive force of roughly 800 ampere-turns per meter of flux path. For most core materials, μ r ≈ 2000 – 6000 {\displaystyle \mu _{r}\approx 2000{\text{–}}6000\,} . So in equation (2) above,

9408-437: The magnets can pinch or puncture internal tissues. Magnetic imaging devices (e.g. MRIs ) generate enormous magnetic fields, and therefore rooms intended to hold them exclude ferrous metals. Bringing objects made of ferrous metals (such as oxygen canisters) into such a room creates a severe safety risk, as those objects may be powerfully thrown about by the intense magnetic fields. Ferromagnetic materials can be magnetized in

9520-416: The material. For a uniformly magnetized cylindrical bar magnet, the net effect of the microscopic bound currents is to make the magnet behave as if there is a macroscopic sheet of electric current flowing around the surface, with local flow direction normal to the cylinder axis. Microscopic currents in atoms inside the material are generally canceled by currents in neighboring atoms, so only the surface makes

9632-477: The material. Not all electromagnets use cores, so this is called a ferromagnetic-core or iron-core electromagnet. This is because the material of a magnetic core (often made of iron or steel) is composed of small regions called magnetic domains that act like tiny magnets (see ferromagnetism ). Before the current in the electromagnet is turned on, the domains in the soft iron core point in random directions, so their tiny magnetic fields cancel each other out, and

9744-412: The name magnetomotive force . For an electromagnet with a single magnetic circuit , Ampere's Law reduces to: This is a nonlinear equation , because the permeability of the core μ varies with B . For an exact solution, the value of μ at the B value used must be obtained from the core material hysteresis curve . If B is unknown, the equation must be solved by numerical methods . However, if

9856-445: The needle of a compass next to a wire carrying current turned so that the needle was perpendicular to the wire. He investigated and discovered the rules which govern the field around a straight current-carrying wire: This sparked a great deal of research into the relation between electricity and magnetism. André-Marie Ampère investigated the magnetic force between two current-carrying wires, discovering Ampère's force law . In

9968-455: The ohmic losses. For this reason, electromagnets often have a significant thickness of windings. Permanent magnet A magnet is a material or object that produces a magnetic field . This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials , such as iron , steel , nickel , cobalt , etc. and attracts or repels other magnets. A permanent magnet

10080-533: The only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to a magnetic field, by one of several other types of magnetism . Ferromagnetic materials can be divided into magnetically "soft" materials like annealed iron , which can be magnetized but do not tend to stay magnetized, and magnetically "hard" materials, which do. Permanent magnets are made from "hard" ferromagnetic materials such as alnico and ferrite that are subjected to special processing in

10192-405: The original circuital law is a line integral of the magnetic field around some closed curve C (arbitrary but must be closed). The curve C in turn bounds both a surface S which the electric current passes through (again arbitrary but not closed—since no three-dimensional volume is enclosed by S ), and encloses the current. The mathematical statement of the law is a relation between

10304-449: The outlines of the core before curving back to enter the next piece of core material, reducing the field strength in the gap. The bulges ( B F ) are called fringing fields . However, as long as the length of the gap is smaller than the cross-section dimensions of the core, the field in the gap will be approximately the same as in the core. In addition, some of the magnetic field lines ( B L ) will take 'short cuts' and not pass through

10416-400: The outlines of the core loop, this allows a simplification of the mathematical analysis. See the drawing at right. A common simplifying assumption satisfied by many electromagnets, which will be used in this section, is that the magnetic field strength B is constant around the magnetic circuit (within the core and air gaps) and zero outside it. Most of the magnetic field will be concentrated in

10528-417: The plates. Second, there is an issue regarding the propagation of electromagnetic waves. For example, in free space , where the circuital law implies that i.e. that the magnetic field is irrotational , but to maintain consistency with the continuity equation for electric charge , we must have To treat these situations, the contribution of displacement current must be added to the current term in

10640-408: The plunger and may make it move. The plunger stops moving when the forces upon it are balanced. For example, the forces are balanced when the plunger is centered in the solenoid. The maximum uniform pull happens when one end of the plunger is at the middle of the solenoid. An approximation for the force F is where C is a proportionality constant, A is the cross-sectional area of the plunger, N

10752-411: The plunger may have a pointed end that fits into a matching recess in the stop. The shape makes the solenoid's pull more uniform as a function of separation. Another improvement is to add a magnetic return path around the outside of the solenoid (an "iron-clad solenoid"). The magnetic return path, just as the stop, has little impact until the air gap is small. An electric current flowing in a wire creates

10864-422: The right hand side is the displacement current as originally conceived by Maxwell, associated with the polarization of the individual molecules of the dielectric material. Maxwell's original explanation for displacement current focused upon the situation that occurs in dielectric media. In the modern post-aether era, the concept has been extended to apply to situations with no material media present, for example, to

10976-471: The same year, the French scientist André-Marie Ampère showed that iron can be magnetized by inserting it in an electrically fed solenoid. British scientist William Sturgeon invented the electromagnet in 1824. His first electromagnet was a horseshoe-shaped piece of iron that was wrapped with about 18 turns of bare copper wire. ( Insulated wire did not then exist.) The iron was varnished to insulate it from

11088-409: The second term dominates. Therefore, in magnetic circuits with an air gap, B depends strongly on the length of the air gap, and the length of the flux path in the core does not matter much. Given an air gap of 1mm, a magnetomotive force of about 796 Ampere-turns is required to produce a magnetic field of 1T. For a closed magnetic circuit (no air gap), such as would be found in an electromagnet lifting

11200-421: The square of the current but only increases approximately linearly with the number of windings, the power lost in the windings can be minimized by reducing I and increasing the number of turns N proportionally, or using thicker wire to reduce the resistance. For example, halving I and doubling N halves the power loss, as does doubling the area of the wire. In either case, increasing the amount of wire reduces

11312-553: The strongest. These cost more per kilogram than most other magnetic materials but, owing to their intense field, are smaller and cheaper in many applications. Temperature sensitivity varies, but when a magnet is heated to a temperature known as the Curie point , it loses all of its magnetism, even after cooling below that temperature. The magnets can often be remagnetized, however. Additionally, some magnets are brittle and can fracture at high temperatures. The maximum usable temperature

11424-707: The surface of the poles. This model assumes point-like poles instead of the really existing surfaces, and thus it only yields a good approximation when the distance between the magnets is much larger than their diameter, so it is useful just for a force between them. Magnetic pole strength of electromagnets can be found from: m = N I A L {\displaystyle m={\frac {NIA}{L}}} The force between two poles is: F = μ 0 m 1 m 2 4 π r 2 {\displaystyle F={\frac {\mu _{0}m_{1}m_{2}}{4\pi r^{2}}}} Each electromagnet has two poles, so

11536-420: The total force on a given magnet due to another magnet is equal to the vector sum of the forces of the other magnet's poles acting on each pole of the given magnet. There are several side effects which occur in electromagnets which must be provided for in their design. These generally become more significant in larger electromagnets. The only power consumed in a DC electromagnet under steady-state conditions

11648-429: The two main attributes of an SMM are: Most SMMs contain manganese but can also be found with vanadium, iron, nickel and cobalt clusters. More recently, it has been found that some chain systems can also display a magnetization that persists for long times at higher temperatures. These systems have been called single-chain magnets. Some nano-structured materials exhibit energy waves , called magnons , that coalesce into

11760-576: The uninsulated wire he used could only be wrapped in a single spaced-out layer around the core, limiting the number of turns. Beginning in 1830, US scientist Joseph Henry systematically improved and popularised the electromagnet. By using wire insulated by silk thread and inspired by Schweigger's use of multiple turns of wire to make a galvanometer , he was able to wind multiple layers of wire onto cores, creating powerful magnets with thousands of turns of wire, including one that could support 2,063 lb (936 kg). The first major use for electromagnets

11872-455: The vacuum between the plates of a charging vacuum capacitor . The displacement current is justified today because it serves several requirements of an electromagnetic theory: correct prediction of magnetic fields in regions where no free current flows; prediction of wave propagation of electromagnetic fields; and conservation of electric charge in cases where charge density is time-varying. For greater discussion see Displacement current . Next,

11984-459: The way their regular crystalline atomic structure causes their spins to interact, some metals are ferromagnetic when found in their natural states, as ores . These include iron ore ( magnetite or lodestone ), cobalt and nickel , as well as the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring ferromagnets were used in the first experiments with magnetism. Technology has since expanded

12096-473: The weakest types. The ferrite magnets are mainly low-cost magnets since they are made from cheap raw materials: iron oxide and Ba- or Sr-carbonate. However, a new low cost magnet, Mn–Al alloy, has been developed and is now dominating the low-cost magnets field. It has a higher saturation magnetization than the ferrite magnets. It also has more favorable temperature coefficients, although it can be thermally unstable. Neodymium–iron–boron (NIB) magnets are among

12208-427: The windings. When a current was passed through the coil, the iron became magnetized and attracted other pieces of iron; when the current was stopped, it lost magnetization. Sturgeon displayed its power by showing that although it only weighed seven ounces (roughly 200 grams), it could lift nine pounds (roughly 4 kilos) when the current of a single-cell power supply was applied. However, Sturgeon's magnets were weak because

12320-421: The wire, a magnetic field is generated. It is concentrated near (and especially inside) the coil, and its field lines are very similar to those of a magnet. The orientation of this effective magnet is determined by the right hand rule . The magnetic moment and the magnetic field of the electromagnet are proportional to the number of loops of wire, to the cross-section of each loop, and to the current passing through

12432-540: The wire. If the coil of wire is wrapped around a material with no special magnetic properties (e.g., cardboard), it will tend to generate a very weak field. However, if it is wrapped around a soft ferromagnetic material, such as an iron nail, then the net field produced can result in a several hundred- to thousandfold increase of field strength. Uses for electromagnets include particle accelerators , electric motors , junkyard cranes, and magnetic resonance imaging machines. Some applications involve configurations more than

12544-410: Was in telegraph sounders . The magnetic domain theory of how ferromagnetic cores work was first proposed in 1906 by French physicist Pierre-Ernest Weiss , and the detailed modern quantum mechanical theory of ferromagnetism was worked out in the 1920s by Werner Heisenberg , Lev Landau , Felix Bloch and others. A portative electromagnet is one designed to just hold material in place; an example

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